When I ran the numbers, it looked like farm land yields + crop prices + land prices made for a bad long-term investment relative to stocks.
Assuming there isn't some ideological reason the Gates are buying farmland, it's probably better viewed as a hedge/diversification -- it may not be a very good investment, yield-wise, but it is decoupled from a lot of other investments.
Small farming is a decent side-gig. Like rental properties, you can earn a good hourly rate on your labor with some capital investment. But the return on purely hands-off investing is minimal or negative.
I know a few people that run small, ~5-acre farms that grow soybeans or corn. From what I gather, they work the equivalent of a few weekends over the summer and earn a few grand an acre after costs. The gotcha seems to be equipment; it's so expensive that one would need huge tracts of land to cover the costs. One guy I know paid someone a % of yield to handle the plowing/harvesting. While my cousin keeps an old, depression-era tractor going and uses that. I imagine some might just lease out the land and collect just enough to cover property taxes.
This seems like a pretty common setup in the midwest. If you travel down some rural back roads, you'll come up on small 2-5 acre plots surrounded by houses. More than likely, these are owned and managed by someone nearby as a side hustle.
Corn yields were ~180 bushels / acre for 2020, and corn prices were [will be, since it is still being sold] $4.85, which comes out to $873 / acre. You might clear a few grand for the entire small field, but even with a second planting of winter wheat I have a hard time imagining making four figures per acre after expenses.
Unless it a specialty crop like pumpkins or is an organic operation, not a chance this happens with corn or soy farms. Your numbers are good. Total operating costs for a corn acre in 2019 were ~700 dollars.
You're estimates sound about right. For my cousin at least, I know what how much he gets paid for his portion of the crop yield each year, but I'm just estimating on the acreage he maintains. So I'm clearly underestimating the amount of land he's working.
Assuming there isn't some ideological reason the Gates are buying farmland, it's probably better viewed as a hedge/diversification -- it may not be a very good investment, yield-wise, but it is decoupled from a lot of other investments.